Here are the science test scores from Ms. O’Donnell’s class:
55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100
Find the MAD.
I don't think that's correct
To find the MAD (mean absolute deviation), follow these steps:
1. Find the mean of the data set:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17 = 79.12
2. Calculate the absolute deviations from the mean for each data point:
|55 - 79.12| = 24.12
|60 - 79.12| = 19.12
|70 - 79.12| = 9.12
|70 - 79.12| = 9.12
|75 - 79.12| = 4.12
|75 - 79.12| = 4.12
|75 - 79.12| = 4.12
|80 - 79.12| = 0.88
|80 - 79.12| = 0.88
|85 - 79.12| = 5.88
|85 - 79.12| = 5.88
|85 - 79.12| = 5.88
|85 - 79.12| = 5.88
|90 - 79.12| = 10.88
|90 - 79.12| = 10.88
|95 - 79.12| = 15.88
|100 - 79.12| = 20.88
3. Find the mean of the absolute deviations:
MAD = (24.12 + 19.12 + 9.12 + 9.12 + 4.12 + 4.12 + 4.12 + 0.88 + 0.88 + 5.88 + 5.88 + 5.88 + 5.88 + 10.88 + 10.88 + 15.88 + 20.88) / 17
MAD = 7.65
Therefore, the MAD for Ms. O’Donnell’s class is 7.65.
To find the Mean Absolute Deviation (MAD) for a set of numbers, you need to follow these steps:
Step 1: Find the mean (average) of the set of numbers.
Step 2: Subtract the mean from each number to find the deviation from the mean.
Step 3: Take the absolute value of each deviation.
Step 4: Find the mean of the absolute deviations.
Now let's calculate the MAD for the given set of scores:
Step 1: Find the mean:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1415
Mean = 1415 ÷ 17 = 83.24 (rounded to two decimal places)
Step 2: Find the deviation from the mean for each number:
|55 - 83.24|, |60 - 83.24|, |70 - 83.24|, |70 - 83.24|, |75 - 83.24|, |75 - 83.24|, |75 - 83.24|, |80 - 83.24|,
|80 - 83.24|, |85 - 83.24|, |85 - 83.24|, |85 - 83.24|, |85 - 83.24|, |90 - 83.24|, |90 - 83.24|, |95 - 83.24|, |100 - 83.24|
Step 3: Calculate the absolute value of each deviation:
|55 - 83.24| = 28.24
|60 - 83.24| = 23.24
|70 - 83.24| = 13.24
|70 - 83.24| = 13.24
|75 - 83.24| = 8.24
|75 - 83.24| = 8.24
|75 - 83.24| = 8.24
|80 - 83.24| = 3.24
|80 - 83.24| = 3.24
|85 - 83.24| = 1.76
|85 - 83.24| = 1.76
|85 - 83.24| = 1.76
|85 - 83.24| = 1.76
|90 - 83.24| = 6.76
|90 - 83.24| = 6.76
|95 - 83.24| = 11.76
|100 - 83.24| = 16.76
Step 4: Find the mean of the absolute deviations:
(28.24 + 23.24 + 13.24 + 13.24 + 8.24 + 8.24 + 8.24 + 3.24 + 3.24 + 1.76 + 1.76 + 1.76 + 1.76 + 6.76 + 6.76 + 11.76 + 16.76) ÷ 17 = 8.43 (rounded to two decimal places)
Therefore, the Mean Absolute Deviation (MAD) for the given set of scores is approximately 8.43.
To find the Mean Absolute Deviation (MAD) of a set of numbers, follow these steps:
1. Find the mean (average) of the numbers in the set. To do this, add up all the numbers and divide by the total count.
Example: Sum of numbers = 55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1370
Total count = 17
Mean = 1370 / 17 = 80.59 (rounded to two decimal places)
2. Find the absolute difference between each number in the set and the mean. To do this, subtract the mean from each number and take the absolute value (ignoring any negative signs).
Example: |55 - 80.59| = 25.59
|60 - 80.59| = 20.59
|70 - 80.59| = 10.59
...
|100 - 80.59| = 19.41
3. Add up all the absolute differences obtained in step 2.
4. Divide the sum of the absolute differences by the total count of numbers in the set.
Let's calculate the MAD for the given test scores:
Step 1: The mean is 80.59
Step 2: Calculating the absolute differences from the mean for each score:
|55 - 80.59| = 25.59
|60 - 80.59| = 20.59
|70 - 80.59| = 10.59
...
|100 - 80.59| = 19.41
Step 3: Summing up the absolute differences: 25.59 + 20.59 + 10.59 + ... + 19.41 = 270.82
Step 4: Dividing the sum by the total count: 270.82 / 17 = 15.93 (rounded to two decimal places)
Therefore, the Mean Absolute Deviation (MAD) of the given test scores is approximately 15.93.